This is probably fine. The connection to DDG will be over HTTPS, so a captured packet would need to be decoded first. And if someone were to manage to break the encryption, then they would also need to know what service you used the password for.

Ultimately, it's more secure to generate locally, but it would be a huge amount of work to get anything usable out of a packet capture

You are not overthinking it. Exploiting this would be a bit more complex than capturing a packet on the wire, but it is possible.

If you intend to use a passphrase for anything important, it's best to generate it locally.

With https as protocol, picked up data packets won't do much harm.
But relying on anything but a local password manager is imho still a bad idea.

Yeah I think I'll just click an icon in my password manager instead.

There are certainly better ideas.

This is probably ok. First of all, they're probably actually doing it in Javascript in the browser. It probably never travels over the network at all. And, if it did, with HTTPS it would be hard to intercept and decrypt except by a government or something.

But, it still gives me the willies to generate a password on a web page. Fundamentally a web browser is still a tool for sending and receiving data over the Internet, and that's not the kind of tool I'd want to be generating something that I don't want other people to know or see.

What happens if there's a bug? If the password is being generated in an app on my local system a badly designed app with a bug could maybe log my newly generated password in a local log file somewhere. If there's a bug in DuckDuckGo's javascript, who knows where that newly generated password might be logged?